Magnetization-vector measurements were performed on field-cooled polycrystalline disks of ${\mathrm{Ni}}_{75}$${\mathrm{Mn}}_{25}$ and ${\mathrm{Au}}_{85}$${\mathrm{Fe}}_{15}$ rotated in a stationary field H. For ${\mathrm{Ni}}_{75}$${\mathrm{Mn}}_{25}$ at 4.2 and 10 K, it is found that the induced anisotropy, which rotates rigidly with the sample for all H, is predominantly unidirectional but with uniaxial and higher-order components that are not negligible. Moreover, the rotational magnetization Mp/${\mathrm{r}}_{\mathit{r}\mathit{o}\mathit{t}}$ is seen to be a unique function of the total effective field Hi/${\mathrm{r}}_{\mathit{e}\mathit{f}\mathit{f}}$ composed vectorially of H plus the anisotropy field ${\mathbf{H}}_{\mathit{K}}$, where M /${\mathrm{r}}_{\mathit{r}\mathit{o}\mathit{t}}$ extends from its saturation value down to zero at Hd/${\mathrm{r}}_{\mathit{e}\mathit{f}\mathit{f}}$=0. For ${\mathrm{Ni}}_{75}$${\mathrm{Mn}}_{25}$ at higher temperatures, it is found that for H above a threshold value the direction of ${\mathbf{H}}_{\mathit{K}}$ changes relative to the rotating sample. This phenomenon is also observed in ${\mathrm{Au}}_{85}$${\mathrm{Fe}}_{15}$ at 4.2 K, and the directional changes of ${\mathbf{H}}_{\mathit{K}}$ are seen to be a dissipative process, which is macroscopically frictional. Qualitative comparisons are made with the available theory.